The present invention relates to methods and apparatus for transforming numerical signal data into a transform domain where certain processing steps can be taken, and for subsequent reconstruction (inverse transform) into the original domain to yield a replica of the original data. Frequently the data is video data, and the signals are video signals.
Signal transforms have been employed to obtain a variety of beneficial results. Important uses in the past have been compression for transmission or storage (also referred to as bandwidth reduction), enhancement for restoration in some sense, detection of some certain phenomenon (e.g., motion detection, edge detection, or center-of-gravity detection), tracking of some certain phenomenon, noise reduction or stripping, and image analysis in general. Prior transforms include the Fourier (with attendant Sine and Cosine transforms), the Haar, the Hadamard, the Slant, block Fourier and Cosine transforms, block Hadamard transform, and the Karhunen-Loeve or Hotelling transform.
By the present invention new transforms are provided, herein termed in the Triangle Transform (for one dimension) and the Pyramid Transform (for two dimensions). The subject Triangle and Pyramid transforms herein disclosed are intended for the purpose briefly identified above, and possess several desirable and useful characteristics individually and in combination not possessed by other transforms. These Triangle and Pyramid transforms are discussed largely as they relate to one- and two-dimensional signal compression for transmission or storage.